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At least 667 records · Page 37
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NASA NTRS1977

Comment on the relation between the nonadiabatic coupling and the complex intersection of potential energy curves

Simple relations are discussed that provide a correspondence between the complex intersection of two potential surfaces and the nonadiabatic coupling matrix element between those surfaces. These are key quantities in semiclassical and quantum mechanical theories of collision induced electronic transitions. Within the two state approximation, the complex intersection is shown to be directly related to the location and magnitude of the peak in the nonadiabatic coupling. Two cases are considered: the avoided crossing between two potential surfaces; and the spin orbit interaction due to a P-2 halogen atom. Comparisons are made between the results of the two-state model and the results of ab initio quantum chemical calculations.

Jaffe, R. L.↗
NASA NTRS1977

Shuttle Program. Euler angles, quaternions, and transformation matrices working relationships

A brief mathematical development of the relationship between the Euler angles and the transformation matrix, the quaternion and the transformation matrix, and the Euler angles and the quaternion is presented. The analysis and equations presented apply directly to current space shuttle problems. The twelve three-axis Euler transformation matrices are given as functions of the Euler angles, the equations for the quaternion as a funtion of the Euler angles, and the Euler angles as a function of the transformation matrix elements.

Henderson, D. M.↗
NASA NTRS1977

Comment on the relation between the nonadiabatic coupling and the complex intersection of potential energy curves

Simple relations are discussed that provide a correspondence between the complex intersection of two potential surfaces and the nonadiabatic coupling matrix element between those surfaces. These are key quantities in semiclassical and quantum-mechanical theories of collision-induced electronic transitions. Within the two-state approximation, the complex intersection is shown to be directly related to the location and magnitude of the peak in the nonadiabatic coupling. Two cases have been considered: (1) the avoided crossing between two potential surfaces, and (2) the spin-orbit interaction due to a 2P halogen atom. Comparisons are made between the results of the two-state model and the results of ab initio quantum chemical calculations.

Jaffe, R. L.↗
NASA NTRS1977

Vibrational and rotational transitions in low-energy electron-diatomic-molecule collisions. I - Close-coupling theory in the moving body-fixed frame. II - Hybrid theory and close-coupling theory: An /l subscript z-prime/-conserving close-coupling approximation

A detailed vibrational-rotational (V-R) close-coupling formulation of electron-diatomic-molecule scattering is developed in which the target molecular axis is chosen to be the z-axis and the resulting coupled differential equation is solved in the moving body-fixed frame throughout the entire interaction region. The coupled differential equation and asymptotic boundary conditions in the body-fixed frame are given for each parity, and procedures are outlined for evaluating V-R transition cross sections on the basis of the body-fixed transition and reactance matrix elements. Conditions are discussed for obtaining identical results from the space-fixed and body-fixed formulations in the case where a finite truncated basis set is used. The hybrid theory of Chandra and Temkin (1976) is then reformulated, relevant expressions and formulas for the simultaneous V-R transitions of the hybrid theory are obtained in the same forms as those of the V-R close-coupling theory, and distorted-wave Born-approximation expressions for the cross sections of the hybrid theory are presented. A close-coupling approximation that conserves the internuclear axis component of the incident electronic angular momentum (l subscript z-prime) is derived from the V-R close-coupling formulation in the moving body-fixed frame.

Choi, B. H.↗
NASA NTRS1977

Theoretical intensity parameters for the vibration-rotation bands of ClO

Intensity parameters for the vibration-rotation bands of ClO were calculated by evaluating matrix elements of the vibrational eigenfunctions using the theoretical dipole moment curve. These vibrational eigenfunctions are based on realistic Klein-Dunham potentials deduced from experimental values (Coxon et al, 1976) for certain vibrational energy levels. The data can be applied to the interpretation of remote or in situ experiments to deduce stratospheric ClO concentrations from vibration-rotation absorption spectra.

Langhoff, S. R.↗
NASA NTRS1977

On the representation matrices of the spin permutation group

A method is presented for the determination of the representation matrices of the spin permutation group (symmetric group), a detailed knowledge of these matrices being required in the study of the electronic structure of atoms and molecules. The method is characterized by the use of two different coupling schemes. Unlike the Yamanouchi spin algebraic scheme, the method is not recursive. The matrices for the fundamental transpositions can be written down directly in one of the two bases. The method results in a computationally significant reduction in the number of matrix elements that have to be stored when compared with, say, the standard Young tableaux group theoretical approach.

Wilson, S.↗
NASA NTRS1978

Quantum mechanical theory of collisional ionization in the presence of intense laser radiation

The paper presents a quantum mechanical formalism for treating ionizing collisions occurring in the presence of an intense laser field. Both the intense laser radiation and the internal electronic continuum states associated with the emitted electrons are rigorously taken into account by combining discretization techniques with expansions in terms of electronic-field representations for the quasi-molecule-plus-photon system. The procedure leads to a coupled-channel description of the heavy-particle dynamics which involves effective electronic-field potential surfaces and continua. It is suggested that laser-influenced ionizing collisions can be studied to verify the effects of intense laser radiation on inelastic collisional processes. Calculation procedures for electronic transition dipole matrix elements between discrete and continuum electronic states are outlined.

Bellum, J. C.↗
NASA NTRS1978

Intensity and pressure shift of the H2 /4,0/ S/1/ quadrupole line

Results are presented for two laboratory measurements of the intensity and central frequency of the (4, 0) S(1) quadrupole line of H2, which were made at pressures of 2.658 and 1.494 atm through a 0.456-km path length. It is found that the absolute line intensity is significantly lower than the value predicted from theoretical matrix elements but is essentially identical to the value derived by Rank et al. (1966). The central-frequency results are shown to verify the pressure shift predicted by McKellar (1974). It is concluded that hydrogen abundances estimated from the equivalent width of the (4,0) S(1) quadrupole line in the spectra of the outer planets will have to be revised upward by nearly a factor of 2.

Bergstralh, J. T.↗
NASA NTRS1977

Derivation of the chemical-equilibrium rate coefficient using scattering theory

Scattering theory is applied to derive the equilibrium rate coefficient for a general homogeneous chemical reaction involving ideal gases. The reaction rate is expressed in terms of the product of a number of normalized momentum distribution functions, the product of the number of molecules with a given internal energy state, and the spin-averaged T-matrix elements. An expression for momentum distribution at equilibrium for an arbitrary molecule is presented, and the number of molecules with a given internal-energy state is represented by an expression which includes the partition function.

Mickens, R. E.↗
NASA NTRS1978

Is photon angular momentum important in molecular collision processes occurring in a laser field

The importance of the rigorous treatment of photon angular momentum in molecular-collision processes occurring in the presence of intense radiation is investigated. An alternate approximate treatment, which essentially neglects the angular momentum coupling between the photon and the molecular degrees of freedom by averaging over the angular dependence of the interaction matrix elements, is presented and applied to a model calculation. The degeneracy-averaged results of this calculation compare remarkably well with the results of a rigorous calculation, from which we conclude (with reservation) that the explicit consideration of photoangular momentum coupling in molecular-collision problems is unnecessary.

Devries, P. L.↗
NASA NTRS1979

Vibrational dependence of pressure induced spectral linewidths and line shifts - Application of the infinite order sudden scattering approximation

The infinite order sudden (IOS) approximation to molecular rotation is applied to simplify the theory of linewidths and shifts in vibration-rotation spectra. This approximation is expected to be most accurate for hard, short-range collisions and is therefore complementary to Anderson theory which is best for weak, glancing collisions. The IOS approximation predicts identical linewidths and shifts for P- and R-branch transitions with the same line number. It also predicts zero line shifts for pure rotational spectra. The dependence of linewidths and shifts on vibrational band is seen to be due mainly to variation in diagonal vibrational matrix elements of the intermolecular potential. Calculations are performed for the 0-0, 0-1, and 0-2 bands of CO perturbed by He, using a theoretical interaction potential with no semiempirical or adjustable parameters; results are in satisfactory accord with experimental data.

Green, S.↗
NASA NTRS1979

Global operators for delta functions - Extension to scattering states and the inclusion of spin

The paper presents an extension of the identities of Hiller, Sucher, and Feinberg for the evaluation of bound-state matrix elements of delta function operators, to scattering states. Attention is given to the technical difficulties encountered in the application of the scattering-state identities and how they can be overcome, including infrared singularities which arise if Coulomb forces are present and the velocity of the incident particle is small. In addition, both the scattering and bound-state identities are generalized to include spin-dependent contact interactions and spin-dependent Hamiltonians. Finally, it is stressed that the identities can be used to improve the accuracy of calculations of interest for diverse physical phenomena, ranging from positron annihilation to hyperfine structure.

Sucher, J.↗
NASA NTRS1980

On the congruent feature in NASTRAN

The congruent feature, which is a capability in NASTRAN that can contribute to significant increases in computational efficiencies, is discussed. The usage of the capability and the software design characteristics affecting it are explained. The factors affecting the efficiency of the feature are pointed out. The details pertaining to the software design of the congruent feature are presented; in particular, the congruent element table is described. Serveral examples employing the congruent feature are considered and comparisons of Element Matrix Generator module computer program update times with and without this feature are presented. The results clearly demonstrate the role of the congruent feature in increasing computational efficiencies and its applicability to large-size problems.

Pamidi, P. R.↗
NASA NTRS1980

Polar nephelometer for atmospheric particulate studies

A polar nephelometer for use in studying atmospheric aerosols was developed. The nephelometer detects molecular scatter from air and measures scattering from very clean air using pure molecular scattering for calibration. A compact system using a folded light path with an air cooled argon laser for the light source was designed. A small, sensitive detector unit permits easy angular rotation for changing the scattering angle. A narrow detector field of view of + or - 1/4 degree of scattering along with a single wavelength of incident light is used to minimize uncertainties in the scattering theory. The system is automated for data acquisition of the scattering matrix elements over an angular range from 2 degrees to 178 degrees of scattering. Both laser output and detector sensitivity are monitored to normalize the measured light scattering.

Hansen, M. Z.↗
NASA NTRS1980

Light scattering by randomly oriented spheroidal particles

A study of the light scattering properties of randomly oriented, identical spheroidal particles is presented. A computation method was developed to integrate the Asano and Yamomoto solution (1975) for scattering from a homogeneous spheroid over all particle orientations; the extinction and scattering cross-sections, the asymmetry factor, and scattering matrix elements are calculated for randomly oriented prolate and oblate spheroids and compared with the calculations for spheres and laboratory measurements. The angular scattering behavior of spheroids is found to be different from that of the spheres for side scattering to backscattering directions, and prolate and oblate spheroids of the same shape parameter have similar angular scattering patterns.

Asano, S.↗
NASA NTRS1980

Polarization characteristics of an altazimuth sky scanner

A theoretical description of the polarization characteristics of an altazimuth sky scanner optical system based on Mueller-Stokes calculus is presented. This computer-driven optical system was designed to perform laboratory studies of skylight and of celestial objects during day or night, and has no space limitations; however, the two parallel 45 deg tilt mirrors introduce some intrinsic polarization. Therefore, proper data interpretation requires a theoretical understanding of the polarization features of the instrument and accurate experimental determination of the Mueller-Stokes matrix elements describing the polarizing and depolarizing action of the system.

Garrison, L. M.↗
NASA NTRS1980

Computational study of alkali-metal-noble gas collisions in the presence of nonresonant lasers - Na + Xe + h/2/pi/omega sub 1 + h/2/pi/omega sub 2 system

The collision of Na with Xe in the presence of both the rhodamine-110 dye laser and the Nd-glass laser is investigated within a quantum-mechanical close-coupled formalism, utilizing ab initio potential curves and transition dipole matrix elements. Both one- and two-photon processes are investigated; the Na + Xe system is not asymptotically resonant with the radiation fields, so that these processes can only occur in the molecular collision region. The one-photon processes are found to have measurable cross sections at relatively low intensities; even the two-photon process has a significant section for field intensities as low as 10 MW/sq cm.

Devries, P. L.↗
NASA NTRS1980

Theoretical treatment of the spin-orbit coupling in the rare gas oxides NeO, ArO, KrO, and XeO

Off-diagonal spin-orbit matrix elements are calculated as a function of internuclear distance for the rare gas oxides NeO, ArO, KrO, and XeO using the full microscopic spin-orbit Hamiltonian, including all one- and two-electron integrals, and POL-CI wave functions comparable to those of Dunning and Hay (1977). A good agreement was found when comparing these results in detail with the calculations of Cohen, Wadt and Hay (1979) that utilize an effective one-electron one-center spin-orbit operator. For the rare gas oxide molecules, it is suggested that the numerical results are a more sensitive test of the wave functions (particularly to the extent of charge transfer) than the exact evaluation of all terms in the full spin-orbit operator.

Langhoff, S. R.↗